2009 International Conference on Networks Security, Wireless Communications and Trusted Computing
A Hybrid Method for Dynamic Local Path Planning
Li Peng, Huang Xinhang, Wang Min
Department of Control Science and Engineering
Huazhong University of Science and Technology
Wuhan 430074, China
[email protected]
Abstract— A hybrid approach for efficiently planning smooth
local paths for mobile robot in an unknown environment is
presented. The single robot is treated as a multi-agent system,
and the corresponding architecture with cooperative control is
constructed. And then a new method of information fusion
DSmT (Dezert-Smarandache Theory) is introduced to deal
with the error laser readings. In order to make A* algorithm
suitable for local path planning, safety guard district search
method and optimizing approach for searched paths are
proposed. Also, the parameters of internal ProportionalIntegral-Derivative (PID) controller in the goto agent smoothes
the path searched by evolutional A* algorithm. Finally, two
kinds of experiments are carried out with Pioneer 2-DXe
mobile robot: one uses the hybrid method proposed in this
paper, the other uses artificial potential field (APF) which is
the classical algorithm for local path planning. The
experimental results reveal the validity and superiority of the
hybrid method for dynamic local path planning. The approach
presented in this paper provides an academic support for path
planning in dynamic environment.
the robots may be trapped in some cases such as with
concave U-shaped barriers. But most studies mentioned
above mainly focus on global path planning and there is few
valid method for local path planning.
This paper presents an efficient hybrid approach for real
time collision-free path planning and grid method is adopted
to depict the environment map. In traditional path planning
studies, the robot is always treated as a single unit. But here
we make the robot a multi-agent system. In this system, each
agent achieves its task and collaborates with other agents for
the same purpose — to find a rational path. When the robot
is commanded to reach an appointed target, in brief, the path
planning agent calculates a temporary path with limited
knowledge about the surroundings with the evolutional A*
algorithm and the behavioral agent smoothes the planned
path using its goto agent. The error readings are wiped off by
filter based on DSmT [5]. And the path is revised once robot
finds an obstacle block the path.
Keywords- path planning, multi-agent, Dezert-Smarandache
It is established that multiple cooperative control in a
single robot involves cooperative control and multi-agent
systems. Cooperative control has a very general meaning,
any complex system developed with multi-agent
architectures may be considered as a cooperative approach.
II.
Theory, A* algorithm, mobile robot.
I.
INTRODUCTION
Mobile robot path planning is one of the most important
topics in robotics research. Point-to-point path planning of
autonomous mobile robot, defined as finding a collision-free
path linking a given start configuration to a goal
configuration, has been extensively explored in last two
decades. Many different methods achieving varying degrees
of success in a variety of conditions/criteria of motion and
environments have been developed.
Path planning for mobile robot is composed of two main
parts: the global path planning and the local path planning.
For global path planning, the entire environment is known
for robot, the robot only needs to compute the path once at
the beginning and then follow the planned path to the target
point. Oppositely for local path planning, the robot only
knows about the area which has been detected itself, it
usually only casually decides the direction to move. There
are many studies on robot path planning using various
approaches, such as the grid-based A* algorithm [1], road
maps [2], cell decomposition [3], and artificial potential field
(APF) [4]. Some of the previous approaches use global
methods to search the possible paths in the workspace,
normally deal with static environments only, and are
computationally expensive when the environment is
complex. Some methods suffer from undesired local minima,
978-0-7695-3610-1/09 $25.00 © 2009 IEEE
DOI 10.1109/NSWCTC.2009.135
MULTI-AGENT ROBOT SYSTEM ARCHITECTURE
Figure 1. Multi-agent robot system.
The multi-agent robot system can be divided into five
subsystems of agents: perception, behavior, path planning,
localization and actuator (Fig.1). The behavioral agent
317
for right status; m(θ2) is the gbbaf for the wrong status;
m(θ1∩θ2) is the gbbaf of conflict mass, it is generated during
the fusion; and m(θ1∪θ2) is the gbbaf of unknown status (it
mainly refers to those areas that still not be scanned at
present).
There are two evidence sources for the filter. The first
source is from the readings themselves. When the robot get a
new group of laser readings, each reading is compared with
its two neighbor readings (left reading and right reading)
except the first and the last reading. For example, if a reading
R is being checking, the left reading is defined as RL and the
right reading is RR, if R≫ RL & R≫ RR or R≪ RR & R≪ RL,
these two situations (shown as Fig.2) means that the reading
R probably is a wrong reading and it need to be fused with
the second source mentioned later. Obviously other
situations mean that R is a right reading and does not need
further fusion.
subsystem includes goto agent and avoid agent. In addition
to all of the above, there is a client agent acting as user
interface. Fig. 1 also depicts the flow of information among
different agents.
The perception agent obtains information about the
environment and about the internal conditions of the robot.
Of course, it includes an error reading filter based on DSmT.
It collects data from the sensors and after getting rid of error
readings adapts them to provide the information requested by
the other agents of the system.
The localization agent locates the robot on the global
map, the path planning agent searches for obstacle free paths.
The behavioral agent subsystem carries out specific
actions, such as avoiding obstacles, going to a point, etc. The
information coming from the localization agent and path
planning agent are used to react or respond to the changes
produced in the robot itself or in the environment. The
following agents have been defined: the goto agent, which is
in charge of taking the robot from the initial to the final
coordinates without considering obstacles; the avoid agent,
which must go around the obstacles when they are found in
the path of the robot.
The actuator agent is responsible for directly using the
robot’s various performance motion components, such as
linear and angular velocity controllers, etc.
Once all the agents are running, the user can request a
task through the client agent which sends the new robot goal
to the path planning agent. Then the path planning agent
decomposes the task into a series of turning point goal and
sends the first target position to the goto agent. Based on this
information and the actual position (obtained from the
localization agent), the goto agent calculates the best linear
and angular speeds to reach the target. On the other hand,
based on the information provided by the localization agent
and laser agent, the avoid agent calculates the linear and
angular speeds needed to dodge the obstacle. At this point
goto agent and avoid agent negotiate in order to decide who
uses the motors. But usually the avoid agent does not need to
work because the path planning has find a collision free path
for robot except accidents. If the target position sent by the
path planning agent is reached, another target position will
be sent to the goto agent.
III.
Figure 2. Two situations of error readings.
The belief assignments of the first source m1(·):
DΘ→[0,1] are constructed by authors as follows:
Re = |RL+RR−2R|∕2;
(1)
Rmax = Max{R, RL, RR};
(2)
m1(θ1) = exp[-5×(Re/Rmax)2];
(3)
(4)
m1(θ2) = 1− m1(θ1);
The second evidence source is from the map which has
been built by the robot. If a laser reading is in one of the two
above mentioned error reading situations, the m1(·)
calculated from the first source will be fused with the m2(·)
of second source. The robot checks the area around of the
reading point which is marked as the potential error reading.
The area is a rectangle with 5×5 grids, and the reading point
is the center grid. The m2(·) of the reading point is calculated
according to the amount of occupied grid in this area.
Suppose N is the amount of occupied grid in this area, the
m2(·) of the second source is computed as:
N < 10,
⎧ N /10,
m2 (θ1 ) = ⎨
,
N ≥ 10;
⎩1
(5)
(6)
m2(θ2) = 1− m2(θ1);
The fusion between m1(·) and m2(·) follows the
combining rules of Proportional Conflict Redistribution rule
2 (PCR2) [7] under the framework of DSmT. The PCR2
formula for k≥2 sources is:
∀( X ≠ φ ) ∈ D Θ mPCR 2 ( X ) =
,
s
c (X )
[
m1 ( X i )] + C ( X ) 12…s
ik12…s
∑ Θ∏
e12…s
i =1
X 1 , X 2 ,…, X s ∈D
X 1 ∩ X 2 ∩…∩ X s = X
(7)
READING FILTER BASE ON DSMT
The DSmT of plausible and paradoxical reasoning
proposed by the authors in recent years allows to formally
combine any types of independent sources of information
represented in term of belief functions [6,7]. And it is able to
solve complex static or dynamic fusion problems, especially
when conflicts between sources become large and when the
refinement of the frame of the problem under consideration,
denoted Θ, becomes inaccessible because of the vague,
relative and imprecise nature of elements of Θ.
Here the Θ is defined as the status of each grid on the
map constructed by the robot. Suppose there are two
elements θ1 and θ2 in the frame of discernment Θ. θ1 means
the reading is wrong and θ2 is defined as right. The hyperpower set is DΘ = {ϕ, θ1∩θ2, θ1, θ2, θ1∪θ2}. Then define
m(θ1) as the general basic belief assignment function (gbbaf)
k12…s =
s
∑ ∏m (X )
X1 ,… X s ∈D Θ i =1
X1 ∩…∩ Xs =φ
i
i
(8)
In this formula, C(X) equals 1 if X involved in the
conflict, or it equals 0. c12…s(X) is the non-zero sum of the
318
column of X in the mass matrix, k12…s is the total conflicting
mass, and e12…s is the sum of all non-zero column sums of all
non-empty sets involved in the conflict.
After fusion, the final gbba of θ1 can be calculated and if
m1(θ1)≥0.8 that means the laser reading which is being
checked is a right reading instead of an error reading.
IV.
on the same line are deleted and then the robot only needs to
store the turning goal points. This method markedly reduces
the memory for storing point-path. The sketch map of
optimizing point-path is shown in Fig.4.
B. Goto agent
It is known that the turning angle of the path calculated
by A* algorithm in the grid map is 45° or 90°. So the path is
not smooth and sometimes the robot cannot follow the
trajectory because of these stark turnings. The goto agent
can solve this problem. It is as shown in Fig.5, the robot’s
walking between two neighbor goal points is under the
charge of goto agent.
The input of goto agent is the target goal point (xi,yi,θi)
and the output is a group of control parameters (v,ω). v is
the robot’s velocity and ω is angular velocity for turning.
The variable d is the distance from current robot’s position
to the target goal point.
PATH PLANNING METHOD
A. Path planning agent
1) Method of path planning agent: The robot plans the
path through path planning agent. After updating the
environmental information, the robot firstly makes use of
evolutional A* algorithm to re-calculate the path if need. The
path from current location to the target point is decomposed
into a series of turning goal point. And then the real path
between every two goal points is smoothed by internal PID
controller.
The A* algorithm is usually used for static global path
planning. There are few applications for dynamic local path
planning in real time because of its large amount of
calculations. In this paper, a simple but very effectual
method is proposed to make the A* suitable for dynamic
local path planning in real time. In most path planning
studies, the robot is abstracted as a point without acreage.
But actually the robot’s radius must be considered in
practical applications. The area near the planned path is the
safety guard district. That means this area must be empty or
the robot cannot pass. The safety guard district is as Fig.3.
Figure 5. Architecture of goto agent.
V.
A user interface platform for experiment is developed by
authors. Pioneer 2-DXe mobile robot is used in experiments.
Two kinds of experiments are carried out: one uses the
hybrid method proposed in this paper, the other uses the
classical algorithm artificial potential field (APF).
An experiment field (size: 4840×3100 mm) is created as
Fig.6. The point of robot is treated as the coordinate origin of
the global map. It is set to the pose of (0,0,0°). The third
parameter is the deflection angle of robot. And the target
goal position is placed near to the right top corner.
Figure 3. Safety guard district.
Once the robot gets a new group of laser readings, each
reading is checked to make sure whether it is in the safety
guard district. If a reading is in this area, it means an obstacle
blocks the way and the path must be re-calculated.
Oppositely, if there is none in the area, well then the path
does not need to be re-calculated. This method reduces the
computations of path planning. The robot only needs to
calculate the path occasionally.
(a)
EXPERIMENTS
Before optimizing (b) After optimizing
Figure 4. Sketch map of optimizing point-path.
Figure 6. Experiment field.
2) Evolutional A* algorithm: The path searched by A*
algorithm is a group of continuous goal points. If the grid is
small, it will spend a large of memory to store the point-path;
and if the goal points are placed too closely, the robot yet
cannot follow the path well because of the limit of its turning
radius. So here the point-path is optimizes. The goal points
Figure 9. APF experimental result
A. Hybrid method experiment
1) The effect of error reading filter: The effect of error
reading filter is verified before the path planning experiment.
The striking dissimilarity between mapping without filter
and mapping with filter is revealed clearly in Fig.7. If there
319
1) In hybrid method experiment, the robot only needs to
store several turning goal points. The planned path is
changed once the robot finds new barriers block the way;
this is expressly shown in Fig.9(c~d).
2) The goto agent performs so perfectly that the real path
of hybrid method experiment is very smooth instead of stark
turnings which is the fault of A* algorithm.
3) Actually, the start position is a concave U-shaped trap.
In hybrid method experiment, the robot can easily walk out
this area and the path is rational. But in APF experiment, the
robot is trapped in local minima; it repeatedly follows the
same trajectory and cannot get out the repetition.
4) The effect of error reading filter based on DSmT is
valid. The maps built with the laser readings are clean and
accurate.
is no filter, the robot cannot find the way to the target goal
because so many barrier-points block the way that there is
not enough space to pass.
(a) Mapping without filter.
(b) Mapping with filter.
Figure 7. Effect of error reading filter
2) Path planning experiment: In order to distinguish the
planned path and the final real path, the real path is only
displayed when the robot arrives at the target goal point.
The experimental result is shown in Fig.8. The circles are
the turning goal points calculated by A* algorithm.
VI.
CONCLUSIONS
This paper has proposed a hybrid approach for planning
smooth paths satisfying dynamic local constraints for robot
in an unknown environment. The single robot is divided into
several synergic agents; among them the most important
agents for path planning are path planning agent and
behavioral agents since their cooperation influences directly
the final result. This paper also presents a valid error reading
filter based on DSmT. Safety guard district search method
and optimizing approach for searched path are proposed. The
results of experiments carried out with Pioneer 2-DXe
mobile robot prove the validity and superiority of the hybrid
method for dynamic local path planning. The application of
the approach presented in this paper to path planning in
completely dynamic unknown environment with moving
objects around the robot will be investigated in the future.
ACKNOWLEDGMENT
This work is supported by the National Natural Science
Foundation of China under grant No. 60675028.
REFERENCES
[1]
Figure 8. Hybrid method experimental result
B. APF experiment
The error reading filter is still used in this experiment for
its important effect. The start position and the target goal
position is the same as the hybrid method experiment. Of
course in this experiment the robot is not a multi-agent
system any more. For this experiment does not need the
behavioral agent subsystem. And then the information flow
becomes unilateral. There are no reciprocities between the
parts in the robot. The APF experimental result is shown as
Fig.9. The trajectory in the center is robot’s real path.
[2]
[3]
[4]
[5]
C. Analysis
It is obviously that the hybrid method proposed in this
paper is a very effectual method for dynamic local path
planning. The experimental results show:
[6]
[7]
320
Chia Hsun Chiang, Po Jui Chiang, Fei, J.C.-C., et al. A comparative
study of implementing Fast Marching Method and A* SEARCH for
mobile robot path planning in grid environment: Effect of map
resolution, Proc. IEEE Workshop Adv. Rob. Soc. Impacts, ARSO.
Hsinchu, Taiwan, Dec 9-11, 2007. pp. 1 – 6
Jung Sungwon, Pramanik Sakti. An efficient path computation model
for hierarchically structured topographical road maps, IEEE Trans
Knowl Data Eng. 2002, 14 (5): 1029-1046.
Rosell Jan, Iniguez Pedro. Path planning using harmonic functions
and probabilistic cell decomposition, Proc IEEE Int Conf Rob Autom.
Barcelona, Spain, Apr 18-22, 2005. pp. 1803-1808.
Zhu Qidan, Yan Yongjie, Xing Zhuoyi. Robot path planning based on
artificial potential field approach with simulated annealing, Proc.
ISDA Sixth Int. Conf. Intelligent Syst. Design Applic., Jinan, China,
Oct 16-18, 2006. pp. 622-627.
Dezert J. Foundations for a new theory of plausible and paradoxical
reasoning. Information and Security, 2002, 9: 13~57
Dezert J, Smarandache F. Advances and Applications of DSmT for
Information Fusion Vol.1. Rehoboth: American Research Press, 2004
Dezert J, Smarandache F. Advances and Applications of DSmT for
Information Fusion Vol.2. Rehoboth: American Research Press, 2006